Jack is thinking of a number. Here are four facts about his number:
a. It is a multiple of 3
b. it had three digits and is a palindrome
C. It is odd
D. At least one digit is 2
What number(s) satisfy the four properties of jacks number?
525
To find the number(s) that satisfy the four properties of Jack's number, we'll go through each property one by one and narrow down the possibilities.
a. It is a multiple of 3:
To find numbers that are multiples of 3, we can start with the smallest three-digit multiple of 3, which is 102, and then count up in increments of 3. So the possible numbers that satisfy this property are: 102, 105, 108, 111, 114, ... and so on.
b. It has three digits and is a palindrome:
A palindrome number reads the same forwards and backwards. Since it is a three-digit palindrome, the first and last digit must be the same. The middle digit can be any number from 0 to 9. So the possible numbers that satisfy this property are: 101, 111, 121, 131, ... and so on.
c. It is odd:
Odd numbers are numbers that are not divisible by 2. So out of the numbers we found in the previous steps, we need to pick the ones that do not end in an even digit (0, 2, 4, 6, or 8). That leaves us with the following numbers: 101, 111, 121, 131, 141, ... and so on.
d. At least one digit is 2:
To satisfy this property, we need to pick the numbers from the previous step that have at least one digit as 2. So the possible numbers that satisfy all four properties are: 121 and 131.
Therefore, the number(s) that satisfy all the properties are 121 and 131.